For regular Volterra kernels the square-root process avoids zero under a time-dependent Feller condition while rough regularly-varying kernels force an atom at zero, with the limit law still having finite negative exponential moments; equivalent martingale measures in the Volterra Heston model exist
Luchko,General fractional integrals and derivatives with the Sonine kernels, Mathematics9(2021), 594
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Proves well-posedness of weighted fractional operators via deformed translation semigroups using amnesia weights, bypassing Bernstein function restrictions.
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Boundary behaviour of the Volterra square-root process
For regular Volterra kernels the square-root process avoids zero under a time-dependent Feller condition while rough regularly-varying kernels force an atom at zero, with the limit law still having finite negative exponential moments; equivalent martingale measures in the Volterra Heston model exist
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A Semigroup Approach to Weighted Weyl-Sonine Operators: Bypassing Bernstein Functions for Well-Posedness
Proves well-posedness of weighted fractional operators via deformed translation semigroups using amnesia weights, bypassing Bernstein function restrictions.